What is the integral of 2/(x(ln(x))^2) ?

The integral of 2/(x(ln(x))^2) is -2/(ln(x))+C

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integral of 2/(x(ln(x))^2)

\int \frac{2}{x ( ln ( x ) ) ^{2}} d x

- \frac{2}{ln ( x )} + C

Solution steps

\int \frac{2}{x ( ln ( x ) ) ^{2}} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 2 \cdot \int \frac{1}{x ( ln ( x ) ) ^{2}} d x

Apply u-substitution

: \int \frac{1}{u ^{2}} d u

= 2 \cdot \int \frac{1}{u ^{2}} d u

Apply the Power Rule

: - \frac{1}{u}

= 2 (- \frac{1}{u})

Substitute back

u = ln (x)

= 2 (- \frac{1}{ln ( x )})

Simplify

2 (- \frac{1}{ln ( x )}) : - \frac{2}{ln ( x )}

= - \frac{2}{ln ( x )}

Add a constant to the solution

= - \frac{2}{ln ( x )} + C

\frac{x ^{2}}{( 2 + x )}

y^{^{''}} - 8 y^{^{'}} - 17 y = 0

\frac{d}{d x} (3 x^{2} y - 2 x^{2} y^{2} + 3 y)

\int_{0}^{\frac{π}{4}} 2 tan^{5} (x) d x

x^{2} - 2 x + 42

What is the integral of 2/(x(ln(x))^2) ?
The integral of 2/(x(ln(x))^2) is -2/(ln(x))+C